Brexit is not a dominant issue for European Union countries, Philip Hammond acknowledged as he called for jobs and prosperity to be the first priority in the negotiations.
The Chancellor told business leaders that the UK had to remember that Brexit was "just one among many challenges" facing the other EU members.
He said the Government had to "focus relentlessly" on the key components of a free trade deal and customs agreement that "minimises friction", with transitional arrangements to avoid a cliff-edge change on the day the UK breaks away from Brussels.
Curbing migration has been a key demand for many Brexit supporters, but Mr Hammond said that while managing the system was important, businesses and public services must be able to recruit from overseas.
In a speech at a Confederation of British Industry dinner, Mr Hammond said the right Brexit outcome would mean: "A comprehensive free trade deal in goods and services that allows the complex value chains that criss-cross our continent to continue to operate smoothly.
"A customs arrangement that minimises friction at the border with a transition that prioritises protection of the free flow of trade across our borders until the agreed long-term arrangements can be put fully in place.
"A future relationship that acknowledges our need to manage migration but allows British businesses and public services to continue to recruit the labour they need to deliver both economic growth and our social objectives."
The deal would acknowledge the "legitimate concerns" of the EU around regulation of financial markets and set up a "co-operative supervisory structure".
"We seek a shared understanding on what the future relationship looks like as early as possible and an agreement with our EU partners that it will be in our mutual interest that there will be a smooth and orderly path to the new arrangements, rather than a disruptive and dangerous cliff-edge.
"Because what businesses and citizens crave more than anything is clarity about the future."
Mr Hammond acknowledged that Brexit was not the main issue on the agenda for many EU countries.
After speaking at a German business conference, he said he was "struck once again during that visit by the 'asymmetry of attention' to this issue. For us, Brexit is the dominant focus; for many of our continental partners, it is just one among many challenges vying for attention".
"We need to remember that fact as we seek their attention to make these arguments," he said.
"And it is incumbent on all of us, in business and in government alike, to go on making the case for a Brexit outcome that protects jobs and prosperity and a transition that takes us to it smoothly."
Mr Hammond urged business leaders to have their say, including by contributing to a new advisory group being set up with Brexit Secretary David Davis and Business Secretary Greg Clark.
Efforts to build bridges with Brussels may have been dealt a blow as a recording emerged of Brexit minister - and prominent Eurosceptic - Steve Baker calling for the EU to be "torn down".
Ministers have repeatedly stressed they want a successful EU to continue after Brexit, but Mr Baker's comments, recorded in 2010, are at odds with that approach.
In the recording, obtained by The Independent, Mr Baker can be seen telling an event organised by the Libertarian Alliance: "I think Ukip and the Better Off Out campaign lack ambition. I think the European Union needs to be wholly torn down.
"The thing is, of course, that is actually impractical unless the whole people of Europe can be persuaded to rise up and vote for politicians who are prepared - in a moderate and consistent and principled and gentle way - to say that the European Union project has merely succeeded in raising economic nationalism to a continental scale."
CBI deputy director-general Josh Hardie said: "Businesses will welcome the Chancellor's commitment to sound public finances at home and a smooth exit from the EU that will support our economy in this time of change.
"Companies will want to see transitional arrangements that prioritise protection of the free flow of trade across borders agreed as soon as possible, and will also want to understand more about how continuity for companies can be secured until long-term arrangements can be established.
"A new migration system allowing firms to access the skills and labour they need to succeed globally is of the utmost importance as the UK seeks to renew its trading relationships around the world, and the Chancellor's commitment to this will be warmly received."
He added: "Now more than ever it's critical that the whole of Government works in partnership with business to make a success of Brexit - that means putting economics before politics to safeguard our economy and prosperity for future generations."